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Rising traffic density, along with autonomy and diversity of vehicles in the air, will fundamentally change the safety environment of the future air transportation system. The change in risk is two-fold: increasing chances of mid-air collisions with non-cooperative objects and increasing chances of crashes over highly populated areas. The changing nature of the vehicles populating the airspace means that civilian aircraft design must now explicitly include considerations of survivability in the event of collision with other vehicles, as well as prevention of damage to people, animals and property on the ground, to a much greater extent than today. This paper offers a preliminary perspective on how MDAO could contribute toward these goals. One of the conclusions is that, in contrast to traditional vehicle design, to accommodate the complexity of the future airspace safely and efficiently, vehicle design requirements, modeling, and design optimization must be closely connected to the properties of the airspace, including those of other vehicles in the air. Thus, the total measure of a vehicle's survivability should include the traditional survivability in malfunction scenarios, combined with new considerations of survivability in collisions and survivability of the public on the ground.

Rapidly expanding unmanned air traffic includes and will continue to include non-cooperative participants. Non-cooperative behavior may be due to technical failure, a lack of appropriate equipment, a careless or malicious operator. Regardless of the cause, the outcome remains: growing density of non-cooperative traffic will increase the risk of collision between unmanned vehicles and aircraft carrying humans. As a result, the degraded safety of airspace may limit access to airspace, with adverse consequences for the traveling public and the economy. Because encounters with small non-cooperative objects, such as birds or wayward drones, can happen too rapidly for an external control system to mitigate them, it is imperative that the aircraft that carry humans survive encounters with non-cooperative vehicles. To-date, design for survivability has been practiced explicitly in the military domain. Survivability against collisions in civil aviation has been limited to tolerances against bird strikes; and these tolerances have proved inadequate on occasion. The growing risk of collision with unmanned vehicles now requires the development of survivability discipline for civilian transport aircraft. The new discipline must be infused into multidisciplinary design methods, on par with traditional disciplines. In this paper, we report on a preliminary study of survivability considerations for the civil aviation domain.

The cumulative degree distributions of transport networks, such as air transportation networks and respiratory neuronal networks, follow power laws. The significance of power laws with respect to other network performance measures, such as throughput and synchronization, remains an open question. Evolving methods for the analysis and design of air transportation networks must address network performance in the face of increasing demands and the need to contain and control local network disturbances, such as congestion. Toward this end, we investigate functional relationships that govern the performance of transport networks; for example, the links between the first nontrivial eigenvalue of a network's Laplacian matrix - a quantitative measure of network synchronizability - and other global network parameters. In particular, among networks with a fixed degree distribution and fixed network assortativity (a measure of a network's preference to attach nodes based on a similarity or difference), those with the small eigenvalue are shown to be poor synchronizers, to have much longer shortest paths and to have greater clustering in comparison to those with large. A simulation of a respiratory network adds data to our investigation. This study is a beginning step in developing metrics and design variables for the analysis and active design of air transport networks.

This paper is one of a set of papers, developed simultaneously and presented within a single conference session, that are intended to highlight systems analysis and design capabilities within the Systems Analysis and Concepts Directorate (SACD) of the National Aeronautics and Space Administration (NASA) Langley Research Center (LaRC). This paper focuses on the specific capabilities of uncertainty/risk analysis, quantification, propagation, decomposition, and management, robust/reliability design methods, and extensions of these capabilities into decision analysis methods within SACD. These disciplines are discussed together herein under the name of Decision Support Methods and Tools. Several examples are discussed which highlight the application of these methods within current or recent aerospace research at the NASA LaRC. Where applicable, commercially available, or government developed software tools are also discussed

Integrating autonomous disciplines into a problem amenable to solution presents a major challenge in realistic multidisciplinary design optimization (MDO). We propose a linguistic approach to MDO problem description, formulation, and solution we call reconfigurable multidisciplinary synthesis (REMS). With assistance from computer science techniques, REMS comprises an abstract language and a collection of processes that provide a means for dynamic reasoning about MDO problems in a range of contexts. The approach may be summarized as follows. Description of disciplinary data according to the rules of a grammar, followed by lexical analysis and compilation, yields basic computational components that can be assembled into various MDO problem formulations and solution algorithms, including hybrid strategies, with relative ease. The ability to re-use the computational components is due to the special structure of the MDO problem. The range of contexts for reasoning about MDO spans tasks from error checking and derivative computation to formulation and reformulation of optimization problem statements. In highly structured contexts, reconfigurability can mean a straightforward transformation among problem formulations with a single operation. We hope that REMS will enable experimentation with a variety of problem formulations in research environments, assist in the assembly of MDO test problems, and serve as a pre-processor in computational frameworks in production environments. Part 1 of two companion papers, discusses the fundamentals of REMS. This paper, Part 2 illustrates the methodology in more detail.

Bilevel problem formulations have received considerable attention as an approach to multidisciplinary optimization in engineering. We examine the analytical and computational properties of one such approach, collaborative optimization. The resulting system-level optimization problems suffer from inherent computational difficulties due to the bilevel nature of the method. Most notably, it is impossible to characterize and hence identify solutions of the system-level problems because the standard first-order conditions for solutions of constrained optimization problems do not hold. The analytical features of the system-level problem make it difficult to apply conventional nonlinear programming algorithms. Simple examples illustrate the analysis and the algorithmic consequences for optimization methods. We conclude with additional observations on the practical implications of the analytical and computational properties of collaborative optimization.

This work is concerned with an approach to formulating the multidisciplinary optimization (MDO) problem that reflects an algorithmic perspective on MDO problem solution. The algorithmic perspective focuses on formulating the problem in light of the abilities and inabilities of optimization algorithms, so that the resulting nonlinear programming problem can be solved reliably and efficiently by conventional optimization techniques. We propose a modular approach to formulating MDO problems that takes advantage of the problem structure, maximizes the autonomy of implementation, and allows for multiple easily interchangeable problem statements to be used depending on the available resources and the characteristics of the application problem.

Historical evolution of engineering disciplines and the complexity of the MDO problem suggest that disciplinary autonomy is a desirable goal in formulating and solving MDO problems. We examine the notion of disciplinary autonomy and discuss the analytical properties of three approaches to formulating and solving MDO problems that achieve varying degrees of autonomy by distributing the problem along disciplinary lines. Two of the approaches-Optimization by Linear Decomposition and Collaborative Optimization-are based on bi-level optimization and reflect what we call a structural perspective. The third approach, Distributed Analysis Optimization, is a single-level approach that arises from what we call an algorithmic perspective. The main conclusion of the paper is that disciplinary autonomy may come at a price: in the bi-level approaches, the system-level constraints introduced to relax the interdisciplinary coupling and enable disciplinary autonomy can cause analytical and computational difficulties for optimization algorithms. The single-level alternative we discuss affords a more limited degree of autonomy than that of the bi-level approaches, but without the computational difficulties of the bi-level methods. Key Words: Autonomy, bi-level optimization, distributed optimization, multidisciplinary optimization, multilevel optimization, nonlinear programming, problem integration, system synthesis

We, discuss criteria by which one can classify, analyze, and evaluate approaches to solving multidisciplinary design optimization (MDO) problems. Central to our discussion is the often overlooked distinction between questions of formulating MDO problems and solving the resulting computational problem. We illustrate our general remarks by comparing several approaches to MDO that have been proposed.

The NASA Langley MDO method evaluation study seeks to arrive at a set of guidelines for using promising MDO methods by accumulating and analyzing computational data for such methods. The data are collected by conducting a series of re- producible experiments. In the first phase of the study, three MDO methods were implemented in the SIGHT: framework and used to solve a set of ten relatively simple problems. In this paper, we comment on the general considerations for conducting method evaluation studies and report some initial results obtained to date. In particular, although the results are not conclusive because of the small initial test set, other formulations, optimality conditions, and sensitivity of solutions to various perturbations. Optimization algorithms are used to solve a particular MDO formulation. It is then appropriate to speak of local convergence rates and of global convergence properties of an optimization algorithm applied to a specific formulation. An analogous distinction exists in the field of partial differential equations. On the one hand, equations are analyzed in terms of regularity, well-posedness, and the existence and unique- ness of solutions. On the other, one considers numerous algorithms for solving differential equations. The area of MDO methods studies MDO formulations combined with optimization algorithms, although at times the distinction is blurred. It is important to

This paper is concerned with a trust region approximation management framework (AMF) for solving the nonlinear programming problem in general and multidisciplinary optimization problems in particular The intent of the AMF methodology is to facilitate the solution of optimization problems with high-fidelity models. While such models are designed to approximate the physical phenomena they describe to a high degree of accuracy, their use in a repetitive procedure, for example, iterations of an optimization or a search algorithm, make such use prohibitively expensive. An improvement in design with lower-fidelity, cheaper models, however, does not guarantee a corresponding improvement for the higher-fidelity problem. The AMF methodology proposed here is based on a class of multilevel methods for constrained optimization and is designed to manage the use of variable-fidelity approximations or models in a systematic way that assures convergence to critical points of the original high-fidelity problem.